Problem 1 Cyclone Tire has produced a new tire with an estimated mean life mileage of 35,000 miles. Management also believes that the standard deviation is 4,500 miles and that tire mileage is normally distributed. To promote the new tire, management is planning to refund a portion of the purchase price if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Cyclone Tire will refund a customer $1 per 100 miles (that is, $0.01 per mile) short of 30,000. For example, if a tire fails at 31,000 miles, Cyclone Tirerefunds $0.However, if a tire fails at 29,500 miles, Cyclone Tire refunds $ 5 (=500 miles short * 0.01 per mile). Run simulation experiment with 1000 simulations to calculate (1) the average cost of the promotion per tire and (2) the probability that Cyclone Tire will refund more than $50 for a tire. Write the code that solves these problems.